1. ## Easy integral help

Can you tell me an easy way (or some easy ways) to solve the following integral? $\int\frac{dx}{sin^2(x)}$
Thanks.

2. Originally Posted by arbolis
Can you tell me an easy way (or some easy ways) to solve the following integral? $\int\frac{dx}{sin^2(x)}$
Thanks.
Hint: Note that $\int \frac {dx}{\sin^2 x}~dx = \int \csc^2 x ~dx$

what do you differentiate to get csc(x)?

3. I don't remember... I guess there is a $ln$ of something.
So let's solve the simpler integral $\int \frac{1}{sin(x)} dx$. To get the one I need, I think a simple substitution will do the job.
I thought of integration by part, but it get more complicated than $\int \frac{1}{sin(x)} dx$. Can you help me a little more?

4. Originally Posted by arbolis
I don't remember... I guess there is a $ln$ of something.
So let's solve the simpler integral $\int \frac{1}{sin(x)} dx$. To get the one I need, I think a simple substitution will do the job.
I thought of integration by part, but it get more complicated than $\int \frac{1}{sin(x)} dx$. Can you help me a little more?
to make Jhevons hint more explicit

what is $\frac{d}{dx}\cot(x)$

This may help...

5. Originally Posted by arbolis
Can you tell me an easy way (or some easy ways) to solve the following integral? $\int\frac{dx}{sin^2(x)}$
Thanks.
Ok, if you don't see it directly try: $u=\tan(x)$ it's very straightforward

6. what is
, I got $\frac{-1}{sin^2(x)}$, therefore $\int\frac{dx}{sin^2(x)}=-cot(x)$. Thanks a lot for your help.